Cantorsdust posted:

As someone who did math competitions throughout childhood, graduated with a degree in mathematics, thought for a long time about being a high school math teacher before abandoning the dream for a better paying career, I can really identify with the article. Mathematics done right is absolutely beautiful. Case in point:


There's tons of times where I would be in the middle of a derivation and start turning down a wrong path, but I would stop. Once things started to get complicated, they got ugly, for lack of a better word. With practice, you can absolutely pick out the moment where you've messed up instead of "following everything to its illogical conclusion." It's the same sense you get when you hear an off key note or start a faltering sentence. But you can't build that sense from rote math problems/teaching, because they're usually far too short. You have to be left to flounder around for a page or two so that you can start to build that sense of when things aren't working out.

Alternatively, you have to learn to sketch out the major derivation steps in your head that you instinctively sense to be true, and then work out a path from there. You might have encountered the term "lemma" in geometry referring to such bridging steps. Again, without "freeform" derivation/proofs, you'll never build that skill.

The thing is that beyond a point, math absolutely gets fun. This was a problem I just thought of yesterday, for which I don't know the answer:

You know primes. Sometimes primes come in pairs only two apart, like 11 and 13, or 29 and 31. It's been proven that there are an infinite number of such "twin prime" pairs. But what about primes appearing three apart? Or four apart? Some number n apart? Are there an infinite number of "n prime" pairs for any n? If not, which n's?

This is a fun question. The answer isn't immediately obvious to me, although I would suspect it's true for all n based on beauty alone. But that's an example of a fun "adult-level" math question that without a proper comprehensive math education, kids would never be able to experience.

fake edit: a bit of googling shows that I was wrong, the number of twin primes is only conjectured to be infinite, but there's strong suspicion that it is. My specific question is called Polignac's conjecture, and was first asked in 1849. Thus far, the best efforts of mathematicians have shown that it is true for at least one number N for N < 246. It remains unanswered. Cool!

Asiina posted:

litany of gulps posted:

Speaking as a former retail employee, the line of authority is not that much different. I went from Wal-Mart management to inner city public school teacher, and it really struck me how similar the policies, procedures, and due process were in both institutions. In both cases, extreme failure resulted in lengthy documentation processes to terminate the employee. I've seen both happen from up close and they were pretty much equal in terms of duration and burden of proof.

temple posted:

A lot of teachers do not have union protections. I really hate the idea that every teacher is sitting behind an army of lawyers if school or district wants to get rid of them.